Final answer:
To find Angle W in a triangle with given side lengths, the Law of Cosines would typically be used. However, with the provided side lengths of WX and XY, Angle W cannot be determined without the length of the third side of the triangle.
Step-by-step explanation:
The problem provided involves finding the measurement of Angle W in triangle WXY given the lengths of the sides. To find Angle W, we can use the Law of Cosines, which is a generalization of the Pythagorean Theorem for any triangle, not just right triangles. The Law of Cosines states for any triangle ABC, with sides a, b, c opposite respective angles A, B, C:
c^2 = a^2 + b^2 - 2ab*cos(C).
In our case, we are looking to find the angle W. We know the lengths of sides WX and XY, which are 11 and 3 inches, respectively. If we call the side opposite Angle W as 'w', the Law of Cosines gives us:
w^2 = 11^2 + 3^2 - 2*(11)*(3)*cos(W).
As we are not given the length of side 'w', and we cannot determine it with the information provided, Angle W cannot be determined with the given lengths of sides WX and XY alone. The problem most likely omits the length of the third side, which is essential for solving this triangle. Without this piece of information, we cannot apply the Law of Cosines to find the measurement of Angle W.